1
NOTICE: this is the author’s version of a work that was accepted for publication in Chemosphere. A definitive
1
version was subsequently published in Chemosphere 119, 83-89, 2015.
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http://dx.doi.org/10.1016/j.chemosphere.2014.05.067 © 2015, Elsevier. Licensed under the Creative 3
Commons Attribution-NonCommercial-NoDerivatives 4.0 International 4
http://creativecommons.org/licenses/by-nc-nd/4.0.
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Predicting sulphate adsorption/desorption in forest soils:
7
evaluation of an extended Freundlich equation
8
9
Jon Petter Gustafsson
a,b,*, Muhammad Akram
b, Charlotta Tiberg
a10
11
aDepartment of Soil and Environment, Swedish University of Agricultural Sciences, Box 7014, 12
750 07 Uppsala, Sweden 13
bDivision of Land and Water Resources Engineering, KTH Royal Institute of Technology, 14
Brinellvägen 28, 100 44 Stockholm, Sweden 15
16
*Corresponding author, E-mail address: jon-petter.gustafsson@slu.se (J.P. Gustafsson).
17
Phone: +46-18-671284 18
19
ABSTRACT 20
Sulphate adsorption and desorption can delay the response in soil acidity against changes in 21
acid input. Here we evaluate the use of an extended Freundlich equation for predictions of 22
pH-dependent SO4 adsorption and desorption in low-ionic strength soil systems. Five B 23
horizons from Spodosols were subjected to batch equilibrations at low ionic strength at 24
different pHs and dissolved SO4 concentrations. The proton coadsorption stoichiometry (η), 25
i.e. the number of H+ ions co-adsorbed for every adsorbed SO42- ion, was close to 2 in four of 26
five soils. This enabled the use of a Freundlich equation that involved only two adjustable 25
parameters (the Freundlich coefficient KF and the non-ideality parameter m). With this model 26
a satisfactory fit was obtained when only two data points were used for calibration. The root- 27
mean square errors of log adsorbed SO4 ranged from 0.006 to 0.052. The model improves the 28
possibility to consider SO4 adsorption/desorption processes correctly in dynamic soil 29
chemistry models.
30 31
Keywords: sulphate adsorption, Spodosols, acidification, Freundlich, pH 32
33
1. Introduction 34
Sulphate adsorption is a process typically associated with the effects of acid deposition on 35
ecosystems. In the 1980s it was established that SO42-
could be adsorbed to iron and 36
aluminium hydrous oxides in soils (Johnson and Todd, 1983; Singh, 1984; Fuller et al., 1985), 37
thus delaying acidification effects in soil and water ecosystems. The major reason for the 38
delayed effect was found to be co-adsorption of H+ during the SO4 adsorption process, a 39
phenomenon described by Hingston et al. (1972). Because the ratio of H+ to SO42- (usually 40
referred to as the proton co-adsorption stoichiometry, η) is higher during SO4 adsorption than 41
it is in the soil solution, SO4 adsorption and desorption greatly affects the response time of 42
ecosystems towards changes in acid deposition (Eriksson, 1988; Eriksson and Karltun, 1994).
43
More recently, it has been shown that SO4 adsorption plays a role not only in mediating the 44
effects of anthropogenic S emissions. For example, Moldan et al. (2012) showed that SO4 45
adsorption and desorption is important in buffering soil systems against extreme climatic 46
events such as ‘sea salt’ episodes. For these reasons, correct understanding of SO4 adsorption 47
and desorption remains an important scope for geochemical research.
48
2
SO4 adsorption in soils involves surface complexation to Fe and Al hydrous oxides as well as 49
poorly crystalline aluminosilicates (imogolite-type materials) (Johnson and Todd, 1983;
50
Gustafsson et al., 1995). Rietra et al. (2001) concluded that for goethite, the mechanism 51
probably involved both inner-sphere and outer-sphere complexes. They constrained the CD- 52
MUSIC surface complexation model of Hiemstra and van Riemsdijk (1996) by use of the 53
following general complexation reaction:
54
FeOH½- + H+ + SO42-↔ FeOSO31½-
+ H2O (1)
55
Alone this reaction implies that η = 1; however, for electrostatic reasons the surface will resist 56
to accommodate this change in charge (-1), especially at low ionic strength; hence some 57
surface groups (FeOH½-) will protonate (to FeOH2½+) causing η to be higher. Recent structural 58
evidence supports the idea that SO42- adsorption on ferrihydrite involves both inner-sphere and 59
outer-sphere complexes (Zhu et al., 2014).
60
Surface complexation models are, however, still difficult to integrate in dynamic models for 61
soil chemistry, not least because they require full knowledge of the system including reactions 62
for all possible competing and interacting ions on the surface. For this reason, simpler 63
relationships consisting of only one or two equations are normally used for predicting the 64
extent of SO4 (and associated H+) adsorption.
65
Some dynamic models (e.g. MAGIC; Cosby et al., 1986 and SMART; Kämäri et al., 1995) 66
use Langmuir equations without explicit consideration of the pH effect. Eriksson (1988), in a 67
rarely cited but pioneering book chapter, suggested a modified Langmuir equation in which 68
each SO42- ion was accompanied by two co-adsorbed H+ ions (i.e. η = 2). This equation was 69
applied to understand the downward migration of acid in Swedish Spodosols in response to 70
acid deposition (Eriksson et al., 1992) and to provide the basis for a dynamic transport model 71
(Eriksson and Karltun, 1994). A similar SO4 adsorption model, which instead used the 72
Temkin equation as a basis, was suggested by Gustafsson (1995). Fumoto and Sverdrup 73
3
(2000, 2001) suggested the use of an extended Freundlich equation with both sulphate and 74
hydrogen ion activities as terms. The model was able to satisfactorily describe pH-dependent 75
SO4 adsorption in an allophanic Andisol. This equation was later modified and included in the 76
dynamic soil model ForSAFE (Wallman et al., 2005) by Martinson and colleagues (Martinson 77
et al., 2003; Martinson and Alveteg, 2004; Martinson et al., 2005).
78
A problem with these empirical equations is, however, that they contain a large number of 79
parameters that have to be optimized. The objective of this paper was to evaluate the use of 80
the extended Freundlich equation using laboratory data from five B horizons from Swedish 81
Spodosols, in which pH and dissolved SO4 concentrations were varied systematically. In 82
particular we tested whether a modified Freundlich equation employing a common value of η 83
= 2 would allow calibration with a minimum of laboratory data and still be able to 84
satisfactorily describe SO4 adsorption.
85
86 87
2. Materials and methods 88
2.1 Soil samples 89
Selected characteristics of the investigated soils are listed in Table 1 and Table 2. All sites 90
were located in coniferous forest, with mostly Pinus sylvestris L. The Tärnsjö soil was sandy 91
whereas the other soils were developed in glacial till with a low (< 5 %) clay content. All soils 92
were classified as Typic Haplocryods. Samples were taken from the uppermost spodic B 93
horizon at all sites except for the Kloten site, at which the investigated sample was from a Bs 94
horizon underlying a thin Bhs horizon that had a larger organic C content.
95
After collection, samples were homogenized and sieved through a 4 mm sieve. They were 96
then kept in doubly sealed plastic bags at 5oC. A small part of the sample was air-dried. The 97
4
dry weight of both field-moist and air-dried samples was determined using conventional 98
methods (105oC for 24 h) to facilitate recalculations to dry-weight basis.
99
100 101
2.2 Laboratory procedures 102
To obtain sulphate adsorption data for calibration of the model, samples were subjected to 103
batch experiments in which 2 g field-most soil was suspended in 32 cm3 solution of various 104
composition as follows:
105
• A background electrolyte of 0.1 mM MgCl2 was present in all samples. This 106
composition was selected to simulate the ionic strength conditions in typical 107
Scandinavian forest soils.
108
• Various additions of MgSO4 (0, 27, 54, 107, 214, 321, and 535 µmol L-1) were made 109
to different samples to produce SO4 adsorption isotherm data.
110
• To produce additional data extending to lower pH values, stock solutions of MgSO4
111
was mixed with H2SO4 in equivalent proportions to produce a second set of isotherm 112
data (additions of 13.5+13.5, 27+27, 54+54, 107+107, 160+160, and 268+268 µmol 113
SO42- L-1). Such additions were not made for the Risfallet B sample, however, as this 114
sample was already quite acid.
115
• Some additional MgSO4/H2SO4 mixtures were prepared and added to the Kloten Bs 116
and Tärnsjö Bs samples to further increase the range of pH values of the data.
117
All equilibrations were performed in duplicate. The batch equilibrations were carried out 118
using 40 cm3 polypropylene centrifuge tubes, and the suspensions were shaken for 24 h in 119
room temperature. The suspensions were then centrifuged. The pH of the supernatant was 120
measured with a Radiometer combination glass electrode. The remaining supernatant solution 121
5
was filtered through a 0.2 µm single-use filter (Acrodisc PF) prior to the analysis of SO4 by 122
ion chromatography (IC) using a Dionex 2000i instrument.
123
To obtain values for initially adsorbed SO4 (Qini), dihydrogen phosphate extraction will 124
quantify the amount of adsorbed SO4 that is in equilibrium with the soil solution (Karltun, 125
1994). Thus, 3.00 g field-moist sample was suspended in 30 cm3 20 mM NaH2PO4 and 126
extracted for 2 h. The extracts were then filtered and subjected to IC analysis as above, after 127
dilution 5 times.
128
To reduce analytical uncertainty, we made frequent use of internal standards both for the IC 129
analysis and for the pH measurement. We estimate the analytical precision to be < 5 % for the 130
IC analysis of SO4, and less than 0.03 units for the pH measurement.
131
Oxalate- and pyrophosphate-extractable Fe and Al were determined according to the 132
procedure of van Reeuwijk (1995), and determined by ICP-OES using a Perkin-Elmer Optima 133
3300 DV instrument. The organic C content of the soils were determined using a LECO 134
CHN-932 analyzer.
135
136
2.3 Model development 137
The model was based on the equation of Martinson et al. (2003), which can be regarded as an 138
extended Freundlich equation. Its mass-action expression can be written as follows:
139
Q = KF · [SO4]m · {H+}n (2)
140
where Q is the amount of adsorbed SO4 (mol kg-1 dry soil), [SO4] is the total dissolved 141
concentration of SO4 (mol L-1), whereas KF, m and n are adjustable parameters; KF is usually 142
termed the Freundlich coefficient, whereas m and n are non-ideality parameters, where m may 143
range between 0 and 1. In a dynamic model there is also a mass-balance equation that governs 144
6
the flux of chemical components between dissolved and sorbed phases. The model of 145
Martinson et al. (2003) applied the following mass-balance equation:
146
[SO42-
] = 0.85·[H+] + 0.15·[BCn+] (3)
147
where the concentration terms are written on an equivalent basis and [BCn+] denotes base 148
cations (Ca2+, Mg2+, K+) . Equation 2 means that every SO42-
ion is accompanied by 1.7 H+ 149
ions during adsorption and desorption (i.e. η = 1.7), a value taken from Karltun (1997), who 150
determined η in a soil suspension at 0.001 M NaNO3. 151
The major disadvantage with this model is the three adjustable parameters KF, m and n, which 152
make proper optimization difficult unless there is a large variation in pH and [SO42-] in the 153
data. If not, different combinations of KF, m and n can lead to equally good fits. Hence large 154
amounts of data need to be collected from one site to sufficiently well constrain the model.
155
In this work, we redefined the mass-action equation (equation 2) so that, instead of viewing 156
H+ and SO42-
as separate components with an own non-ideality parameter m and n, we 157
assumed that the relationship between their non-ideality parameters was constrained by the 158
value of η, according to:
159
m = n · η (4)
160
This results in the following modified extended Freundlich equation:
161
Q = KF · ([SO42-
] ·{H+}η)m (5)
162
After taking the logarithm of both sides, and substituting log{H+} for pH, we obtain:
163
log Q = log KF + m · (log[SO42-
] - η·pH) (6)
164
Equation 6 implies that a plot of log Q vs. log[SO42-] - η·pH should lead to a straight line with 165
the slope m and the intercept KF. Although this equation still has three adjustable parameters, 166
it can be brought down to two if a common value of η is employed. In this work, we 167
7
hypothesized that the value of η in forest soils can be set to 2. This would also provide a direct 168
link between the mass-action and mass-balance equations and therefore simplify the mass- 169
balance equation (equation 3), since co-adsorbing base cations would no longer need to be 170
considered:
171
[SO42-
] = [H+] (7)
172
where, to be consistent with equation 3, the concentration terms are written on an equivalent 173
basis.
174
To obtain additional evidence for the value of η, we (i) optimized the value of η for the batch 175
experiment data of this study (c.f. below), and (ii) set up a simulation using the CD-MUSIC 176
model for ferrihydrite at pH 5. The model was based on the work of Rietra et al. (2001) who 177
investigated the use of the CD-MUSIC model for SO4 adsorption onto goethite (see equation 178
1). The model was calibrated for ferrihydrite using the SO4 adsorption data of Davis (1977), 179
Swedlund and Webster (2001) and Fukushi et al. (2013) and by using parameters for surface 180
charging estimated by Tiberg et al. (2013), see the Supplementary Content for details. This 181
model was defined in Visual MINTEQ (Gustafsson, 2013) and used to calculate the η value at 182
pH 5 and at different ionic strengths ranging from 0.4 mM (the conditions of the batch 183
experiment of this study) to 10 mM. Because η is sensitive to the presence of competing ions 184
in the system, we included also PO4 and Si at environmentally “realistic” concentrations, c.f.
185
Supplementary Content. The results show that the η value was approximately 1.95 at low 186
ionic strength (Fig, 1) and remained above 1.9 also at an ionic strength of 0.001 M (Fig. 1).
187
The result agrees with the results of Ishiguro et al. (2006), who obtained an η value close to 188
2.0 at low ionic strength for an allophanic Andisol.
189
To calibrate the model for the soils under study, we used three different optimization 190
strategies:
191
8
1. Unconstrained fit. All three adjustable parameters (KF, m and η) of equation 6 were 192
fitted using linear regression of log Q vs. log[SO42-
] - η·pH with the trendline tool in 193
Microsoft Excel. The value of Q was calculated as the sum of initially adsorbed SO4
194
as determined by phosphate extraction (Qini) and SO4 sorbed during the experiment.
195
2. Constrained fit. Fitting was made as described above for the unconstrained fit, except 196
that the η value was fixed at 2.
197
3. 2-point calibration (2PC) fit. Mean results from only two samples were used during 198
optimization. These samples should be sufficiently different in terms of pH and [SO42-
199
] to produce well-constrained values of KF and m. We used (i) the sample to which 200
only 0.1 mM MgCl2 had been added (with relatively high pH and low [SO42-
] ) and (ii) 201
the sample to which 0.1 mM MgCl2, 0.27 mM MgSO4 and 0.27 mM H2SO4 had been 202
added (relatively low pH and high [SO42-
] ). For the Risfallet sample, the latter sample 203
was not available; instead the second sample used was the one to which 0.1 mM 204
MgCl2 + 0.535 mM MgSO4 had been added.
205
To compare the goodness-of-fit, the RMSE (root-mean square errors) of the simulated values 206
of log Q were determined, using the measured log Q values as the reference.
207
208
3. Results 209
The five B horizons investigated were different concerning their capability of retaining SO4, 210
as could be deduced from the phosphate-extractable SO4 values (Table 2). The Kloten and 211
Risbergshöjden soils can be regarded as strongly SO4-adsorbing, whereas the three other soils 212
contained rather low levels of initially adsorbed SO4. This is consistent with oxalate- 213
extractable Fe and Al, which were highest in the Kloten and Risbergshöjden soils. When SO4
214
was added, these soils sorbed the largest amounts (Fig. 2). In both soils, and also in the 215
Tärnsjö B horizon, addition of MgSO4 alone caused the pH to increase (Fig. 2), probably 216
9
because SO4 adsorption caused co-adsorption of H+ that was greater than the release of H+ 217
brought about by Mg2+ adsorption in the samples. Further, the SO4 adsorption isotherms 218
differed depending on whether SO4 was added as MgSO4 or as a mixture of MgSO4 and 219
H2SO4. The latter solutions resulted in stronger SO4 adsorption because of the lower pH 220
obtained.
221
Concerning the extended Freundlich model, optimization using the unconstrained fitting 222
method resulted in excellent fits for the Kloten and Risbergshöjden soils (Table 3, Fig. 3), 223
whereas the fit was poorer particularly for the Risfallet soil. The optimized η value was close 224
to 2 for all soils except for the Österström soil, for which η was found to be 3.83. The reason 225
why η was high for the Österström soil could not be established; however, as was mentioned 226
above the optimization of 3 parameters often leads to poorly constrained fits. It is also 227
possible that some other process not accounted for by our simple model approach (e.g.
228
precipitation as Al or Fe sulphate minerals at low pH) could be responsible. In the other four 229
soils the finding that η ≈ 2 is consistent with the assumption that the non-ideality parameters 230
of H+ and SO42-
are interrelated (equation 4).
231
As η was ≈ 2 in four of the five soils, the constrained fitting method (where η was fixed at 2) 232
led to very similar fits (Fig. 3, Table 3). Also the 2PC method, for which only two samples 233
were considered, led to good fits that in most cases were similar. The RMSE values (in terms 234
of log Q) ranged from 0.006 to 0.052. As concerns the fits of the 2PC approach, consistent 235
deviation between model and measurements was found only for the Österström sample; this is 236
probably related to the higher η for this sample (as mentioned above) for the unconstrained fit.
237
238
4. Discussion 239
The surface complexation modeling exercise suggests that the use of η = 2 for SO4 adsorption 240
should be possible in low-ionic strength systems such as acid forest soils, as η > 1.9 under 241
10
realistic conditions (pH = 5 and I < 0.001 M). This is further supported by the evaluation of 242
the unconstrained model fit, as the optimized η value was close to 2 for four out of five soils.
243
This brings down the number of adjustable model parameters to two, which is important since 244
it makes it easier to calibrate the Freundlich model. However, the result for the Österström 245
sample (optimized η = 3.83) shows that this may not strictly hold true for all soils. Additional 246
research is required to investigate whether this is due to the omission of some other process in 247
the model (e.g. precipitation) or whether it may simply be caused by uncertainties or errors in 248
one or more of the input parameters (measured pH, dissolved and adsorbed SO4).
249
The results can be compared to earlier studies in which pH-dependent empirical adsorption 250
equations have been evaluated. Both Eriksson (1988) and Gustafsson (1995) developed 251
models in which it was assumed that η ≈ 2, but they were based on the Langmuir and Temkin 252
equations respectively. The former author did not present any experimental data in support of 253
the Langmuir equation. Gustafsson (1995) used a sequential leaching procedure that produced 254
data in support of the Temkin equation, according to which there should be a linear 255
relationship between log[SO42-
] - 2·pH and Q. However, this model did not correctly 256
reproduce the data of the present study (see Fig. S1). Our data are more consistent with the 257
Freundlich equation, which assumes a relationship between log[SO42-
] - 2·pH and log Q. This 258
is in agreement with the conclusions of Fumoto and Sverdrup (2000). The reason why 259
Gustafsson (1995) obtained a better fit with the Temkin equation may be due to the sequential 260
leaching procedure used, which could have dissolved interacting ions, thus yielding incorrect 261
results. The experimental method in the present study should be better suited for producing 262
reliable results since only one equilibration was used; thus the dissolution of interacting ions 263
was minimized.
264
The non-ideality parameter m for SO4 ranged from 0.11 to 0.24 in this study; this can be 265
compared to the results of Martinson et al. (2005) for 16 soils, according to which m ranged 266
11
from 0.0043 to 0.13. In addition, the non-ideality parameter for H+ was similarly low in the 267
study of Martinson et al. (2005) (range 0.017 to 0.11), whereas in the present study it ranged 268
from 0.21 to 0.47. We believe that our results are more realistic, as the low parameter values 269
reported by Martinson et al. (2005) predict substantial SO4 adsorption even at pH > 9, which 270
does not agree with results for pure Fe oxides (see, e.g. Fukushi et al. 2013). A possible 271
reason to the different results is that dissolution of both interacting ions and sorbents may 272
have occurred in the procedure used by Martinson et al. (2003, 2005), as this included 273
collection of SO4 adsorption data at very low pH (3.8 and 4). There may also be other possible 274
reasons for the differences, relating e.g. to the numerical optimization methods used.
275
Accurate determination of the non-ideality parameters is important, as these determine to 276
what extent the adsorbed SO4 (and co-adsorbed H+) pool changes in response to a change in 277
influent H+ and SO42-
concentrations. The low parameter values reported by Martinson et al.
278
(2005) would imply that SO4 adsorption/desorption is not very important for soil chemical 279
dynamics, whereas the results of the present study suggest it to be much more significant.
280
An aspect not considered in the model is competition effects from, e.g. organic matter and 281
phosphate. Indirectly the Freundlich model may account for the current state as concerns 282
competition. If, however, the concentration of the competitors change over a long-term 283
period, this will cause effects that cannot be described by the simple model presented here.
284
Although the suggested model is potentially useful to generate SO4 adsorption parameters 285
from a limited number of laboratory data, an additional limitation is that the method requires a 286
wide range in dissolved SO4 and/or pH to be successful. Hence, soils that initially are low in 287
pH and high in dissolved SO4 will be difficult to parameterize, as the sorption experiment 288
method will not bring about substantial differences in chemical conditions. Ideally, it should 289
be possible to calibrate the SO4 adsorption model without any laboratory data at all, but 290
instead using other measurements (e.g. organic C, extractable Fe+Al, total geochemistry) 291
12
made in soil inventories etc. An interesting observation in this regard is the relatively small 292
variation in m, which may make it possible to use a generic m value and only use a 293
relationship between soil properties and the KF value. To address this issue, the SO4
294
adsorption properties of a larger number of well-characterized soils need to be investigated 295
using the model.
296
297
5. Conclusions 298
Sulphate adsorption could be described well by a modified pH-dependent Freundlich 299
equation, in which the non-ideality parameters for the sulphate and hydrogen ion activities 300
were interconnected by the η (proton co-adsorption stoichiometry) value. This enabled the 301
number of fitted parameters to be reduced from 3 to 2 when using a fixed value for η. By use 302
of the CD-MUSIC surface complexation model it was found that the η value in a competitive 303
system on ferrihydrite was > 1.9 at low ionic strength, i.e. close to 2. This was supported by 304
unconstrained fitting for the soils of this study, for which the optimized value of η for four out 305
of five soils was close to 2. When using a fixed value of η = 2, it was possible to use a two- 306
point calibration (2PC) method and still obtain satisfactory descriptions of SO4 adsorption 307
across a range of pH and dissolved SO4 concentrations. These results may simplify the use of 308
the extended Freundlich equation for SO4 adsorption/desorption in dynamic soil chemistry 309
models, both because only a small number of laboratory input data are required to calibrate 310
the model, and because the mass balance equation for SO4 adsorption can be simplified by 311
only considering charge neutralization by H+. 312
313
Acknowledgments 314
13
We thank Bertil Nilsson for assistance on the laboratory. This work was funded by the 315
Swedish Research Council Formas through QWARTS (Quantifying weathering rates for 316
sustainable forestry), project no. 2011-1691.
317
318
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384 385
16
Fig. 1. Proton co-adsorption stoichiometry (η) for SO4 adsorption on ferrihydrite as a function of ionic strength, at pH 5, as simulated by the CD-MUSIC model. Conditions are detailed in Appendix A.
1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2
0.0001 0.001 0.01
n (Proton co-adsorption stoichiometry)
Ionic strength (mol L-1)
0 1 2 3 4 5 6 7 8 9 10
0 100 200 300 400 500
Q(mmol kg-1)
Dissolved SO4(µmol L-1)
MgSO4 MgSO4+H2SO4
5.29
5.00
4.65
Kloten
0 0.5 1 1.5 2 2.5
0 100 200 300 400 500 600
Q(mmol kg-1)
Dissolved SO4(µmol L-1)
MgSO4 MgSO4+H2SO4 4.74
4.60 4.22
Österström
0 1 2 3 4 5 6 7 8 9
0 100 200 300 400 500
Q(mmol kg-1)
Dissolved SO4(µmol L-1)
MgSO4 MgSO4+H2SO4 4.78
4.94 4.46
Risbergshöjden
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0 100 200 300 400 500 600
Q(mmol kg-1)
Dissolved SO4(µmol L-1)
MgSO4 4.96
4.82
Risfallet
Fig. 2. Adsorbed sulphate (Q) as a function of dissolved SO4 in response to different addtions of MgSO4 or MgSO4+H2SO4 (see text). Points are observations and lines are model fits using the 2PC (two-point calibration) optimization. The figures shown are the pH values recorded after additions of 0 and 500 µmol L-1 SO42-
. 0
0.5 1 1.5 2 2.5 3 3.5 4 4.5
0 100 200 300 400 500 600
Q(mmol kg-1)
Dissolved SO4(µmol L-1)
MgSO4 MgSO4+H2SO4 5.38
5.65 4.70
Tärnsjö
y = 0.17882x + 0.23793 R² = 0.99600
-2.5 -2.45 -2.4 -2.35 -2.3 -2.25 -2.2 -2.15 -2.1 -2.05 -2
-15 -14.5 -14 -13.5 -13 -12.5
log Q
log [SO4] - 1.98*pH
y = 0.17831x + 0.24874 R² = 0.99599
-2.5 -2.45 -2.4 -2.35 -2.3 -2.25 -2.2 -2.15 -2.1 -2.05 -2
-15 -14.5 -14 -13.5 -13 -12.5
log Q
log [SO4] - 2*pH
y = 0.14755x + 0.23474 R² = 0.97687
-3.5 -3.4 -3.3 -3.2 -3.1 -3 -2.9 -2.8 -2.7 -2.6 -2.5
-24 -23 -22 -21 -20 -19
log Q
log [SO4] - 3.83*pH
y = 0.19218x - 0.41704 R² = 0.95490
-3.5 -3.4 -3.3 -3.2 -3.1 -3 -2.9 -2.8 -2.7 -2.6 -2.5
-16 -15 -14 -13 -12 -11
log Q
log c - 2*pH
y = 0.14469x - 0.19673 R² = 0.99523
-2.6 -2.5 -2.4 -2.3 -2.2 -2.1 -2
-15.5 -15 -14.5 -14 -13.5 -13 -12.5
log Q
log [SO4] - 2.15*pH
y = 0.14797x - 0.25624 R² = 0.99451
-2.6 -2.5 -2.4 -2.3 -2.2 -2.1 -2
-14.5 -14 -13.5 -13 -12.5 -12
log Q
log [SO4] - 2*pH
Kloten
Österström
Risbergshöjden
Fig. 3. Plots of log Q vs. log[SO42-] - η·pH for the five soils (Kloten, Österström,
Risbergshöjden, Risfallet and Tärnsjö) and linear regression results for the unconstrained fit (left column) and the constrained fit (right column).
y = 0.10852x - 1.14333 R² = 0.95908
-3 -2.95 -2.9 -2.85 -2.8 -2.75 -2.7
-17 -16.5 -16 -15.5 -15 -14.5 -14
log Q
log c - 2.35*pH
y = 0.11092x - 1.29686 R² = 0.95888
-3 -2.95 -2.9 -2.85 -2.8 -2.75 -2.7
-15.5 -15 -14.5 -14 -13.5 -13 -12.5
log Q
log c - 2*pH
y = 0.23550x + 0.62150 R² = 0.97022
-3.5 -3.3 -3.1 -2.9 -2.7 -2.5 -2.3 -2.1
-16 -15 -14 -13 -12
log Q
log [SO4] - 1.97*pH
y = 0.23404x + 0.63781 R² = 0.97019
-3.5 -3.3 -3.1 -2.9 -2.7 -2.5 -2.3 -2.1
-16 -15 -14 -13 -12
log Q
log [SO4] - 2*pH
Risfallet
Tärnsjö
Table 1
Location and properties of soils Site Location (Lat,
Long)
Parent material
Horizon sampled
Sampling depth (cm)
Kloten 59.91oN
15.25oE
Glacial till Bs 14-24
Österström 62.64oN 16.71oE
Glacial till Bs 5-15
Risbergshöjden 59.72oN 15.05oE
Glacial till Bs 4-13
Risfallet 60.34oN 16.21oE
Glacial till Bs 7-15
Tärnsjö 60.14oN 16.92oE
Sand Bs 2-16
Table 2
Chemical properties of the investigated soil samples Sample Organic C pH(MgCl2)a Feoxb
Fepyrb
Aloxb
Alpyrb
PSO4c
% mmol kg-1
Kloten 2.56 5.00 147 70 659 280 4.18
Österström 2.23 4.77 88 53 171 117 0.61
Risbergshöjden 2.58 4.78 124 29 554 175 4.55
Risfallet 2.30 4.96 155 86 265 168 1.29
Tärnsjö 0.72 5.38 46 15 120 65 0.78
apH measured in the 0.10 mM MgCl2 extract without SO4 addition (see Methods section)
bSubscripts ox and pyr denote oxalate and pyrophosphate extracts, respectively
cPhosphate-extractable SO4
Table 3
Best-fit results for the extended Freundlich model
Sample Fit a KF m ηb r2
RMSE c
Kloten Unconstr 1.74 0.179 1.98 0.996 0.006
Constr 1.77 0.178 2 0.996 0.006
2PC 2.09 0.184 2 - 0.010
Österström Unconstr 1.72 0.148 3.83 0.977 0.025
Constr 0.383 0.192 2 0.955 0.035
2PC 0.536 0.201 2 - 0.045
Risbergshöjden Unconstr 0.636 0.145 2.15 0.995 0.005
Constr 0.554 0.148 2 0.995 0.005
2PC 0.634 0.152 2 - 0.006
Risfallet Unconstr 0.0719 0.108 2.35 0.959 0.015
Constr 0.0505 0.111 2 0.959 0.015
2PC 0.0445 0.107 2 - 0.016
Tärnsjö Unconstr 4.18 0.236 1.97 0.970 0.034
Constr 4.34 0.234 2 0.970 0.034
2PC 4.43 0.237 2 - 0.052
aUnconstrained, constrained and 2-point calibration (2PC) fits, respectively
bValues in italics were fixed during optimization
cRoot-mean square error of the simulated log Q values, as compared to the measured log Q.
Supplementary content
J.P. Gustafsson, M. Akram, C. Tiberg. Predicting sulfate adsorption/desorption in forest soils: evaluation of an extended Freundlich equation for use in a dynamic soil chemistry model
Table S1
Surface complexation reactions and constants used in the CD-MUSIC model for ferrihydrite.
Reaction (∆z0, ∆z1, ∆z2)a log Kb Data source(s)
FeOH½- + H+ ↔ FeOH2½+ (1,0,0) 8.1 Dzombak & Morel (1990)
Fe3O½- + H+ ↔ Fe3OH½+ (1,0,0) 8.1 Assumed the same as above
FeOH½- + Na+ ↔ FeOHNa½+ (0,1,0) -0.6 Hiemstra & van Riemsdijk (2006)
Fe3O½- + Na+ ↔ Fe3ONa½+ (0,1,0) -0.6 ”
FeOH½- + H+ + NO3-↔ FeOH2NO3½- (1,-1,0) 7.42 ”
Fe3O½- + H+ + NO3-↔ Fe3OHNO3½- (1,-1,0) 7.42 ”
FeOH½- + H+ + Cl-↔ FeOH2Cl½- (1,-1,0) 7.65 ”
Fe3O½- + H+ + Cl-↔ Fe3OHCl½- (1,-1,0) 7.65 ”
2FeOH½- + 2H+ + PO43-↔ Fe2O2PO22- + 2H2O (0.46,-1.46,0) 27.59 Tiberg et al. (2013) 2FeOH½- + 3H+ + PO43-↔ Fe2O2POOH- + 2H2O (0.63,-0.63,0) 32.89 ”
FeOH½- + 3H+ + PO43-↔ FeOPO3H2½- + H2O (0.5,-0.5,0) 30.23 ” FeOH½- + H+ + SO42-↔ FeOSO31½-
+ H2O (0.65,-1.65,0) 9.65 Rietra et al. (2001), this study 2FeOH½- + H4SiO4↔ Fe2O2Si(OH)2- + 2H2O (0.45,-0.45,0) 5.04 Gustafsson et al. (2009)c
a The change of charge in the o-, b- and d-planes respectively.
b Two or three numbers indicate binding to sites with different affinity, the percentages of which are within brackets (c.f. text).
cThis constant was updated using the more recent model of Tiberg et al. (2013)
Table S2
Data sets used for optimisation of sulfate surface complexation constants for ferrihydrite (Fh)
ID number Source Total SO4 (M) Fh concentration
(mM)
Equilibration time (h) Background electrolyte
Fh-SO4-01 Davis (1977) 1 × 10-5 1 4 0.1 M NaNO3
Fh-SO4-02 Swedlund and Webster (2001) 2.08 × 10-4 0.96 ” ”
Fh-SO4-03 ” 1.82 × 10-3 ” ” ”
Fh-SO4-04 Fukushi et al. (2013) 2 × 10-4 1.96 ” ”
Fh-SO4-05 “ 2 × 10-4 ” “ 0.01 M NaNO3
Fh-SO4-06 ” 1 × 10-4 ” ” 0.1 M NaNO3
Fh-SO4-07 ” 1 × 10-4 ” ” 0.01 M NaNO3
Table S3
Intrinsic surface complexation constants for sulfate adsorption on ferrihydrite (standard deviations in parantheses). Weighted average equilibrium constants are shown, with the 95 % confidence interval (italics in parantheses).
Data set log K, FeOSO3 VY
a
Fh-SO4-01 9.97 (0.009) 5.7
Fh-SO4-02 9.79 (0.014) 13.6
Fh-SO4-03 9.68 (0.012) 2.0
Fh-SO4-04 9.68 (0.007) 4.9
Fh-SO4-05 9.38 (0.010) 6.3
Fh-SO4-06 9.76 (0.007) 9.6
Fh-SO4-07 9.32 (0.008) 25.2
Weighted averages 9.65 (9.57, 9.73)
aWeighted sum of squares, according to Herbelin and Westall (1999)
Table S4
Conditions assumed for the surface complexation modeling exercise on ferrihydrite to calculate η (proton coadsorption stoichiometry)
Parameter Assumed value
Ferrihydrite concentration 0.89 g L-1 ( = 10 mmol Fe L-1)
pH 5.0
Dissolved SO4a
10 µmol L-1 Dissolved PO4
a 0.05 µmol L-1
Dissolved H4SiO4a
100 µmol L-1
Dissolved Mg2+a 100 µmol L-1
Dissolved Cl-a 100 µmol L-1
Dissolved Naa 0 µmol L-1
aDissolved concentrations without any added SO4 and at the lowest ionic strength (0.4 mM). By use of the “fixed total dissolved” option in Visual MINTEQ the total system concentrations of SO4, PO4 and H4SiO4 were determined and kept constant in all simulations. Ionic strengths were increased by adding equivalent amounts of Na+ and Cl- to the solutions up to 10 mM. To calculate η, a further 0.1 mM SO4 was added and the total H+ concentration of all surface species was calculated in the absence and presence of added SO4, and divided with that of the calculated concentration of adsorbed SO4.
Fig. S1. Plot of Q vs. log[SO4
2-] - 2·pH for the Kloten soil (according to the Temkin model of Gustafsson, 1995) and linear regression results.
References
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y = 2.4037x + 39.492 R² = 0.9762
3 4 5 6 7 8 9 10
-15 -14.5 -14 -13.5 -13 -12.5
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All samples
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